useful for the technical students

1. EARTH SUN ANGLE &
OBERVER ANGLE
PREPARED BY:-
SONU KUMAR BAIRWA

2. Sun Earth Angles
• The angle between the earth- sun line and the earth’s equatorial
plane is known as the angle of declination.
• This varies with the date; and the orbital velocity of the earth
traveling around the elliptic plane also varies slightly.
• The two angles that completely describe the sun position are the
solar altitude b, measured from 0° to 90° above the horizon, and
the solar azimuth f, measured from 0° to 180° from the south with
positive sign eastwards and negative sign westwards.
• To determine these two angles from data on Latitude, date and
time, the following calculation is carried out:
• Instead of being expressed in time units, true solar time can be
expressed in angular terms related to the earth"s rotation as the
hour angle, H, where
•

3. • Since in one minute the earth rotates 0.25°.
Values a.m. are +ve and p.m. +ve. Then,
• sin b = cos L cos d cos H + sin L sin d
• And
• sin f = (cos d sin H) / cos b

4. • L
• Latitude, degrees
• D
• declination, degrees (northern hemisphere =+ve, southern hemisphere = -
ve)
• Values of b and f may be available from tables in publications or graphical
techniques for finding them are also available.

5. OBSERVER SUN ANGLES
• The Solar Altitude (αsαs) measures the angle between the
central ray from the Sun (beam radiation), and a horizontal plane
containing the observer. Note that the subscript ``ss'' is there to
indicate that the altitude relative to the observer of the Sun.
• This will become important in evaluating the altitude angles of
other objects projected onto the sky dome, like buildings,
overhangs, wing walls, and arrays of solar receivers.
sinαs=sinδsinϕ+cosδcosϕcosωsinαs=sinδsinϕ+cosδcosϕcosω
cosαssinγs=−cosδsinωcosαssinγs=−cosδsinω
αs=sin−1[sinδsinϕ+cosδcosϕcosω]
•

6. • The Zenith Angle (θzθz) is the geometric complement
of the solar altitude angle.
• We direct your attention to the use of θθ here, as the
general concept of the angular deviation of the Sun's
ray from the normal projection of a surface is called
the angle of incidence, θθ.
• In effect, the zenith angle represents the angle of
incidence for a horizontal surface.
• Recall: "normal" means perpendicular to a surface.
cosθz=sinδsinϕ+cosδcosϕcosωcosθz=sinδsinϕ+cosδco
sϕcosω
θz=cos−1[sinδsinϕ+cosδcosϕcosω]
•

7. • The Solar Azimuth measures the angle on the
horizontal plane between the meridian of the 0
degrees axis (South, for the Northern hemisphere,
opposite Down Under) and the meridional projection
of the Sun's central beam (the Sun's meridian).
• The convention we will use is also used in the
advanced design tools for solar energy, TRNSYS (UW-
Madison: Transient eNergy Simulation Software),
PVSyst, and SAM (NREL: System Advisor Model).
• The angle varies from 0 degrees at the South-pointing
coordinate axis to
±180±180
• degrees. East (earlier than noon) is negative and west
(later than noon) is positive in this basis.